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arXiv · 2411.16889

Classification of Semigraphical Translators

Francisco Martín·Mariel Sáez·Raphael Tsiamis·Brian White
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Abstract

We complete the classification of semigraphical translators for mean curvature flow in $\mathbb{R}^3$ that was initiated by Hoffman-Mart\'in-White. Specifically, we show that there is no solution to the translator equation on the upper half-plane with alternating positive and negative infinite boundary values, and we prove the uniqueness of pitchfork and helicoid translators. The proofs use Morse-Rad\'o theory for translators and an angular maximum principle.

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Francisco Martín, Mariel Sáez, Raphael Tsiamis, Brian White. 2024-11-25. Classification of Semigraphical Translators. https://arxiv.org/abs/2411.16889

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